A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio

Synaptic transmission between pairs of retinal amacrine cells in culture

We have examined synaptic transmission between isolated pairs of chick GABAergic amacrine cells, maintained in sparse culture and identified by their binding of an amacrine cell-selective antibody. Using the perforated- patch method to whole-cell clamp both cells of a pair, postsynaptic currents were examined for step depolarizations of the \u27presynaptic\u27 cell. Synaptic transmission, frequently reciprocal, was calcium dependent and reversibly blocked by bicuculline. Postsynaptic currents, excluding those due to ohmic electrical coupling, were elicited only for presynaptic voltage steps positive to about -40 mV and were always very noisy, suggesting that they were summed from relatively small numbers of quanta. Postsynaptic currents continued well after the termination of the 100 msec presynaptic voltage step when the step was to -10 mV, or positive to this value. This result is interpreted to imply that presynaptic calcium concentration remains elevated after the membrane is returned to its holding potential. When presynaptic voltages were kept low or else presynaptic voltage was uncontrolled, spontaneous quantal events mediated by GABA(A) receptors could often be seen. Quanta rose quickly (less than 4 msec) and decayed with a mean time constant of 19.3 msec. The amplitude distributions of quantal currents were positively skewed, sometimes showing rare quanta of exceptionally large amplitude. Peak conductance per quantum was about 300 pS, corresponding to the simultaneous opening of only 17 GABA(A) channels and corresponding to a net flux of only 32 x 103 Cl- ions per millivolt of driving force. Estimates of the maximum sustained release rate at individual release sites suggest an upper bound of between 19 and 42 quanta per second

Electrogenic Na-Ca exchange clears Ca\u3csup\u3e2+\u3c/sup\u3e loads from retinal amacrine cells in culture

Calcium influx into cultured retinal amacrine cells is followed by a small, slow, inward current that we show here results from the operation of electrogenic Na-Ca exchange. The activity of the exchanger is shown to correlate with the magnitude of the Ca2+ load and to depend on both the Ca2+ and Na+ gradients. Li+ is unable to substitute for Na+ and in the absence of Na+, slow tail currents are almost entirely suppressed. A rapid change in [K+](o) does not affect the activity of the exchanger, suggesting that only Na+ and Ca2+ are transported. The ratio of charge entering as Ca2+ current to the charge entering as exchange current is highly variable between cells. We suggest that variability results from a variable fraction of Ca2+ load, we estimate typically 40%, being removed by a process other than Na-Ca exchange. This process is likely to involve internal buffering or sequestration since inhibition of the plasmalemmal Ca2+ATPase does not increase the fraction of Ca2+ expelled by the exchanger. Ca2+ loading performed in the absence of Na+(o) generates smaller exchange charge the longer the delay in returning Na+(o) to the neuron. About 30% of exchange charge is lost for a delay of 1 sec

Non-Contextual Hidden Variables and Physical Measurements

For a hidden variable theory to be indistinguishable from quantum theory for finite precision measurements, it is enough that its predictions agree for some measurement within the range of precision. Meyer has recently pointed out that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can thus be effectively nullified if only finite precision measurements are considered. We generalise this result: it is possible to ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.Comment: Typo corrected. Final version: to appear in Phys. Rev. Let

The auxiliary use of LANDSAT data in estimating crop acreages: Results of the 1975 Illinois crop-acreage experiment

The author has identified the following significant results. It was found that classifier performance was influenced by a number of temporal, methodological, and geographical factors. Best results were obtained when corn was tasselled and near the dough stage of development. Dates earlier or later in the growing season produced poor results. Atmospheric effects on results cannot be independently measured or completely separated from the effects due to the maturity stage of the crops. Poor classifier performance was observed in areas where considerable spectral confusion was present

Maximally Causal Quantum Mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman

Structural contributions to the pressure-tuned charge-density-wave to superconductor transition in ZrTe3: Raman scattering studies

Superconductivity evolves as functions of pressure or doping from charge-ordered phases in a variety of strongly correlated systems, suggesting that there may be universal characteristics associated with the competition between superconductivity and charge order in these materials. We present an inelastic light (Raman) scattering study of the structural changes that precede the pressure-tuned charge-density-wave (CDW) to superconductor transition in one such system, ZrTe3. In certain phonon bands, we observe dramatic linewidth reductions that accompany CDW formation, indicating that these phonons couple strongly to the electronic degrees of freedom associated with the CDW. The same phonon bands, which represent internal vibrations of ZrTe3 prismatic chains, are suppressed at pressures above ~10 kbar, indicating a loss of long-range order within the chains, specifically amongst intrachain Zr-Te bonds. These results suggest a distinct structural mechanism for the observed pressure-induced suppression of CDW formation and provide insights into the origin of pressure-induced superconductivity in ZrTe3.Comment: 6 pages, 5 figure

Classical Lie algebras and Drinfeld doubles

The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of simple Lie algebras is discussed. This structure is determined by two disjoint solvable subalgebras matched by a pairing. For the two nilpotent positive and negative root subalgebras the pairing is natural and in the Cartan subalgebra is defined with the help of a central extension of the algebra. A new completely determined basis is found from the compatibility conditions in the double and a different perspective for quantization is presented. Other related Drinfeld doubles on C are also considered.Comment: 11 pages. submitted for publication to J. Physics

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure